In combinatorics, a lattice path L in the d-dimensional integer lattice of length k with steps in the set S, is a sequence of vectors such that each consecutive difference lies in S. A lattice path may lie in any lattice in , but the integer lattice is most commonly used. An example of a lattice path in of length 5 with steps in is . (Wikipedia).
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From playlist Recreational Math Videos
This video introduces lattice paths and explains how to determine the shortest lattice path.
From playlist Counting (Discrete Math)
Lattice Paths Application: Driving
This video provides an example of lattice paths.
From playlist Counting (Discrete Math)
Determine the Number of Shortest Lattice Paths Under Various Conditions
This video provides examples on how to determine the shortest lattice paths under various conditions.
From playlist Counting (Discrete Math)
Pell Number Lattice Path Enumeration and visual recurrence formula (synthwave; visual proof)
This synthwave enumeration shows all of the lattice paths with steps (1,1), (-1,1) and (2,0) from the origin (0,0) to the line y = n-1. The number of such lattice paths is counted by the Pell numbers, and we use the visual enumeration to show how to produce the (linear) recurrence formula
From playlist Discrete Mathematics Course
paths on a lattice (or how many ways from A to B in d dimensions) #SoME2
We present a solution to the problem of finding the number of shortest paths that traverse an n-by-n-by-...-by-n lattice in d dimensions. We start our journey in two dimensions and uncover two distinct yet related routes toward the solution of the problem for a given sized square lattice.
From playlist Summer of Math Exposition 2 videos
Longest Simple Path - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Pascal's Triangle from Lattice Paths (synthwave; enumeration; combinatorics)
This synthwave enumeration shows all of the northeast lattice paths on the 5x5 integer grid. The number of such lattice paths to a point (a,b) is counted by the binomial coefficient {a+b choose a}, as is discussed in this video: https://youtu.be/KYpOoA2D63w. So as you watch this video, Pas
From playlist Discrete Mathematics Course
Walking city streets: Catalan Closed Form (visual proof from lattice paths)
In this video, we show how to provide a closed form for the number of northeast lattice paths to the point (n,n) that don't pass below the line y=x. The number of such lattice paths is counted by the famous Catalan numbers. For other videos discussing lattice paths (and those mentioned i
From playlist Combinatorics
Amit Patel (5/1/21): Edit Distance and Persistence Diagrams Over Lattices
We build a functorial pipeline for persistent homology. The input to this pipeline is a filtered simplicial complex indexed by any finite lattice, and the output is a persistence diagram defined as the Mobius inversion of a certain monotone integral function. We adapt the Reeb graph edit d
From playlist TDA: Tutte Institute & Western University - 2021
The Binomial Recurrence from Lattice Paths (visual proof)
This short animated proof demonstrates one combinatorial proof for the recurrence satisfied by the binomial coefficients. #mathshorts #mathvideo #math #mtbos #manim #animation #theorem #visualproof #proof #iteachmath #mathematics #binomialcoefficients #latticepaths #discretemath
From playlist Proof Writing
Mod-01 Lec-14 Lattice Vibrations (Continued) Phonon thermal conductivity
Condensed Matter Physics by Prof. G. Rangarajan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist NPTEL: Condensed Matter Physics - CosmoLearning.com Physics Course
P. Di Francesco: "Triangular Ice Combinatorics"
Asymptotic Algebraic Combinatorics 2020 "Triangular Ice Combinatorics" P. Di Francesco - University of Illinois & IPhT Saclay Abstract: Alternating Sign Matrices (ASM) are at the confluent of many interesting combinatorial/algebraic problems: Laurent phenomenon for the octahedron equatio
From playlist Asymptotic Algebraic Combinatorics 2020
Elliptic Curves - Lecture 14b - Elliptic curves over the complex numbers
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Noriyoshi Sukegawa: On the diameter of polyhedra and related topics
Many questions about the behavior of the simplex method remain open today. The (combinatorial) diameter of polyhedra provides a lower bound on the worst-case complexity of the simplex method. The aim of this talk is to overview previous results on the diameter of polyhedra from various per
From playlist Workshop: Tropical geometry and the geometry of linear programming
PotW: Counting Lattice Paths from (0, 0) to (16, 16) [Combinatorics]
Make sure to check out our blog for a full solution transcript! http://centerofmathematics.blogspot.com/2019/07/problem-of-week-7-16-19-counting.html
From playlist Center of Math: Problems of the Week
Dana Randall: Sampling algorithms and phase transitions
Markov chain Monte Carlo methods have become ubiquitous across science and engineering to model dynamics and explore large combinatorial sets. Over the last 20 years there have been tremendous advances in the design and analysis of efficient sampling algorithms for this purpose. One of the
From playlist Probability and Statistics